"You lied to me, and you cheated on me, and you offended me.

This construction is perfectly fine, since you are intentionally using the commas and the repeated use of "you" for emphasis.

Otherwise, I agree with the answers and comments you have received so far, except that they apply more to people who do not know about the general use of commas, which you obviously do.

With such very short sentences, you do not need a comma to separate them. Using a comma slows down the reading of the sentence, or introduces pauses. The use or non use of commas can represent whether the speaker is saying these three sentences all in one go (without any pause between them) or whether he is speaking slower, with a pause in between each statement.

The repetition of you obviously changes the emphasis, as this is a rhetorical effect or device. Using you three times hammers home the fact that it was you who did this.

I would not use a comma if you omitted the second two yous because I personally try to avoid using a comma to separate what I would consider non-independent clauses (and cheated on me)—although I notice I did this anyway in the second sentence of this answer (and introduces pauses). My answer implies that punctuation, including comma usage, can be somewhat personalized or up to the writer.

The original is ordered in a slightly odd way; usually, the last item in the list is the most important, but I think most people would consider being cheated on of considerably more importance than merely being offended — which could reasonably be a side effect of either of the two previous, well, "offenses". A more natural ordering would be "You offended me, and you lied to me, and you cheated on me." I'll be assuming this for the rest of the answer.

The repetition of "and you" (as well as "me"), as others have noted, makes this list more emphatic. Removing any of those words makes it less so, although not enormously less so; there's still some verbal punch to "You offended, lied to, and cheated on me" (the shortest form that preserves the original meaning). If you remove "me" from the repetition, you cannot also remove the prepositions here, one of which forms a phrasal verb ("cheat on") and the other of which distinguishes between two different meanings of the verb "lie" (deceive vs. rest). That is:

• ^ok You offended, and you lied to, and you cheated on me.

• ^* You offended, and you lied, and you cheated me.

Normally, context would be enough to tell that "You lied." (without "to me") is referring to deception, and indeed it is enough here too to generally grasp that meaning. Grammatically, though, if you omit all but one of the objects in a repetitive sentence like this, they're all tied to the same object more closely, and as Hellion has noted in comments elsewhere, "lied me" doesn't work here. The meaning can be reconstructed despite the poor structure, but it's best to avoid that mistake in the first place.

It's also often best to avoid omitting repeated objects (or subjects), even though it's grammatical, because it requires more thought to understand properly. It's also more formal, so in this context, it sounds odd to be using such a precise economy of words in what is certainly an emotional statement.

You can omit commas in the original without any real problem (perhaps a slight loss of dramatic pauses), but if you take out the conjunctions this no longer works:

• ^ok You offended me and you lied to me and you cheated on me.

• ^* You offended me lied to me you cheated on me.

  (If you want to get across the idea of someone incoherent with rage, so upset they simply can't talk grammatically, the latter might work. Otherwise, no.)

• You have offended me by lying to me and by cheating on me.

• By lying to me and by cheating on me, you have also offended me.

• I am offended that you would lie to me and would cheat on me.

I typically will attempt to eliminate the use of commas as they cause the reader to pause, and for some readers this interrupts their comprehension.

Eliminating the "you" will also eliminate the ownership of the actions "lie" and "cheated". Ownership is actually very important for the reader, as it gives a solid sense of who does what, what is, and who it is.

No. In a list of items you need an "and" or a comma, but not both. This is correct with and's:

You lied to me and you cheated on me and you offended me.

And this is correct with commas. Note that there is still an "and" between the last two items.

You lied to me, you cheated on me, and you offended me.

Also, there is a lot of debate on whether there should be a comma between the second phrase (you lied to me) and the word "and". I included the comma, and doing this is known as "The Oxford Comma". However, you could leave that comma out and say

You lied to me, you cheated on me and you offended me.

And (depending on who you ask) this is also correct.

To answer your second question, no you can leave out the word "you" and the meaning is unchanged. You could even further shorten it the way @peter said You lied, cheated, and offended me. All three would have equivalent meaning.

First, the first "and" is unnecessary. I'm not completely sure whether it's incorrect, but it sounds strange and can be omitted. You definitely need the commas, but you can indeed omit the "you"s.

You offended me, by lying and cheating on me.

The first "and" is unnecessary. "and" is used to join two sentences.